1/1×5+1/5×9+1/9×13+...+1/2009×2013

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1/1×5+1/5×9+1/9×13+...+1/2009×20131/1×5+1/5×9+1/9×13+...+1/2009×20131/1×5+1/5×9+1/9×13+...+1/2009×20

1/1×5+1/5×9+1/9×13+...+1/2009×2013
1/1×5+1/5×9+1/9×13+...+1/2009×2013

1/1×5+1/5×9+1/9×13+...+1/2009×2013
答:
1/(1×5)+1/(5×9)+1/(9×13)+...+1/(2009×2013)
=(1/4)×(1-1/5+1/5-1/9+1/9-1/13+.+1/2009-1/2013)
=(1/4)×(1-1/2013)
=(1/4)×(2012/2013)
=503/2013